Destruction of interstellar dust occurs predominantly in supernova shock waves in the warm neutral/ionized medium (density congruent-to 0.25 cm-3, temperature congruent-to 10(4) K). Recent theoretical developments and laboratory data for sputtering processes and grain-grain collisional vaporization allows us to better evaluate the grain destruction rate in interstellar shocks in the warm medium. We find that, independent of composition, grain denstruction in supernova blast waves is dominated by nonthermal sputtering for shock velocities > 50 km s-1 and less-than-or-equal-to 150 km s-1 and thermal sputtering at higher shock velocities. We use a detailed scheme for the vaporization of grains colliding at high velocities (upsilon(s) greater-than-or-equal-to 20 km s-1) and show that the grain-grain collision destruction process is only dominant for shock velocities of less-than-or-equal-to 50-80 km s-1 and is less important than previously assumed. Nevertheless, the grain-grain destruction rates are of order 30%-90% of the sputtering rates at 100 km s-1 < upsilon(s) < 200 km s-1 and are important in vaporizing the cores of grains. Detailed results for grain destruction as a function of grain size and composition are presented. In particular, we consider Mathis, Rumpl, & Nordsieck size distribution of silicate and carbonaceous (amorphous carbon/graphite) grains. We also present results for silicon carbide, iron, ice, and porous test particles. For carbonaceous grains we find that the fractional destruction is less-than-or-equal-to 0.29, and for silicate it is less-than-or-equal-to 0.45, for upsilon(s) less-than-or-equal-to 200 km s-1. We have calculated grain lifetimes, using the three-phase model of the interstellar medium, and find lifetimes of 4 x 10(8) yr for carbonaceous grains and 2.2 x 10(8) yr for silicate grains. Given that the typical stardust injection timescale is 2.5 x 10(9) yr, we conclude that efficient mechanisms for grain growth in the interstellar medium must exist in order that a significant fraction of the refractory elements be incorporated in dust, as observed. Therefore, although our improved model has less vaporization of dust due to grain-grain collisions, sputtering still destroys dust efficiently and grain mantle growth in the interstellar medium is required, a conclusion reached in previous models of grain destruction in the interstellar medium. Carbonaceous mantles on silicate grains can protect the silicate cores from sputtering destruction in interstellar shock waves, provided that the protective mantles can efficiently reform in the interstellar medium. Also, if the grains are porous the postshock grain velocities are lower than for solid particles, and grain destruction is reduced. Porosity and mantling may increase the grain lifetime by factors of approximately 3 and approximately 3-4, respectively. The fraction of interstellar silicon in silicate stardust is therefore less-than-or-equal-to 0.25, but more silicon might be depleted in the form of a grain mantle.
